Eddie Howe was the favourite to succeed Neil Lennon at Parkhead but the talks between him and Celtic collapsed last Friday.
With Celtic still on the lookout for a new man at the helm, Postecoglou has now emerged as the leading candidate for the job.
Bosnich insisted that his fellow Australian sets his teams up to play an attractive brand of football and encourages his men to press high and play out from the back.
The former Premier League goalkeeper is of the view that Postecoglou is capable of adapting his tactical set-ups according to the different situations that his team find themselves in.
“In terms of his playing philosophy, I used to have debates with him because he was a big fan of this”, Bosnich told Sky Sports News.
“It’s about the process and that’s more important than the result, but he’ll find out very, very quickly as I’m sure he has done in Japan – that the result is going to define exactly how he goes here.
“He loves playing attractive football, he loves his team to press high, he loves to have centre-backs that can play out from the back.
“He prefers to play a 4-3-3, sometimes that can be a 4-2-3-1, but if there’s one word to describe him in terms of his coaching, that would be adaptable.”
After losing the Scottish Premiership title to Rangers in the season gone by, the Hoops will be determined to rope in a manager who can turn them into champions again next season.
